cp's OEIS Frontend

A320673 Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod i)] for i = 1..k (where [] is an Iverson bracket).

%I A320673 #14 Dec 12 2022 15:00:22
%S A320673 1,50,52,104,114,3460,12298,29442,31368,856592,1713184,54822416,
%T A320673 109578256,109644832,219156512,219289664,438313024,438579328,
%U A320673 876626048,877158656,1034367516,1753252096,1754317312,112208117792,113290248736,224416235584,226580497472
%N A320673 Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod i)] for i = 1..k (where [] is an Iverson bracket).
%C A320673 In other words, the binary representation of a term of this sequence encodes the first divisors and nondivisors of this term respectively as ones and zeros.
%C A320673 Is this sequence infinite?
%C A320673 See A320674 and A320675 for similar sequences.
%e A320673 The first terms, alongside their binary representation and the divisors encoded therein, are:
%e A320673   n  a(n)   bin(a(n))        First divisors
%e A320673   -  -----  ---------------  --------------------
%e A320673   1      1  1                1
%e A320673   2     50  110010           1, 2, 5
%e A320673   3     52  110100           1, 2, 4
%e A320673   4    104  1101000          1, 2, 4
%e A320673   5    114  1110010          1, 2, 3, 6
%e A320673   6   3460  110110000100     1, 2, 4, 5, 10
%e A320673   7  12298  11000000001010   1, 2, 11, 13
%e A320673   8  29442  111001100000010  1, 2, 3, 6, 7, 14
%e A320673   9  31368  111101010001000  1, 2, 3, 4, 6, 8, 12
%o A320673 (PARI) is(n) = my (b=binary(n)); b==vector(#b, k, n%k==0)
%o A320673 (Python)
%o A320673 from itertools import count, islice
%o A320673 def A320673_gen(startvalue=0): # generator of terms >= startvalue
%o A320673     return filter(lambda n:not any(int(b)==bool(n%i) for i,b in enumerate(bin(n)[2:],1)),count(max(startvalue,0)))
%o A320673 A320673_list = list(islice(A320673_gen(),10)) # _Chai Wah Wu_, Dec 12 2022
%Y A320673 Cf. A070939, A320674, A320675.
%K A320673 nonn,base
%O A320673 1,2
%A A320673 _Rémy Sigrist_, Oct 19 2018